"We have looked at this thing from every which way," Thomas told the insider newsletter. "It doesn't make sense to get in. We don't see a chance to win. I don't want to be a second candidate against an incumbent."
His decision means Mourdock will likely have a clear shot against Lugar in the May primary. The state filing deadline is Feb. 21.
Thomas also said he would not endorse Lugar or Mourdock.
In 2010, Thomas spent $600,000 out of his own pocket to challenge then-Rep. Mark Souder (R-Ind.). Thomas lost his primary bid to Souder by about 14 points in what was a crowded GOP field.
United We Dream protesters carry a mock coffin to the office of Sen. Ted Cruz, R-Texas, in the Dirksen Senate Office Building on Monday, July 21, 2014, to hold one of their "funeral services for the Republican Party" due to GOP positions on immigration. The immigration reform group visited several other Senate Republican offices to hold similar funeral services.